A Recursive Algorithm described here generates consecutive sequences of Goldbach sets GP(m) = {p,p’| p + p = 2m} where p and p’ are prime numbers and m >2, toward the proof of the Strong Goldbach Conjecture (SGC). The approach suggested here is based on the fundamental principle of mathematical induction and uses rather elementary set-theoretical technique and the property of shift-invariance of Goldbach sets with respect to specific mappings. The main idea of this work is to develop a recursive algorithm for building the sequence of consecutive Goldbach sets {GP(k) | k = 3, 4, …, m} representing solutions to the system of Goldbach equations {x + y = 2k| k is in [3, m]} in the intervals of integers I = [3, 2k – 3] The validity of the algorithm is based on the proved here recursive formula, generating Goldbach set GP(m) given the created consecutive sets GP(k), which are not empty for all k = 3,4, …, m-1, due to inductive assumption. The paper includes some discussion of the Diophantine geometry of Goldbach sets related to Goldbach function, twin- and t-primes, as well as the text of the computer script in R with realization of the suggested recursive algorithm.